Question: Complete the recursive formula of the arithmetic sequence $13, 6, -1, -8,...$. $c(1)=$
Solution: The first term is $13$ and the common difference is $-7$. ${-7\,\curvearrowright}$ ${-7\,\curvearrowright}$ ${-7\,\curvearrowright}$ $13,$ $6,$ $-1,$ $-8,...$ This is the recursive formula of $13, 6, -1, -8,...$ $\begin{cases} c(1)=13 \\\\ c(n)=c(n-1)+(-7) \end{cases}$